Kinetics of the radical-radical reaction, O(3P(J)) + OH(X2Pi omega) --> O2 + H, at temperatures down to 39 K

The kinetics of the reaction between O atoms and OH radicals, both in their electronic ground state, have been investigated at temperatures down to ca. 39 K. The experiments employed a CRESU (Cinétique deRéaction en Ecoulement Supersonique Uniforme) apparatus to attain low temperatures. Both reagents were created using pulsed laser photolysis at 157.6 nm of mixtures containing H2O and O2 diluted in N2 carrier gas. OH radicals were formed by both direct photolysis of H2O and the reaction between O(1D) atoms and H2O. O(3P) atoms were formed both as a direct product of O2 photolysis and by the rapid quenching of O(1D) atoms formed in that photolysis by N2 and O2. The rates of removal of OH radicals were observed by laser-induced fluorescence, and concentrations of O atoms were estimated from a knowledge of the absorption cross-section for O2 at 157.6 nm and of the measured fluence from the F2 laser at this wavelength. To obtain a best estimate of the rate constants for the O + OH reaction, we had to correct the raw experimental data for the following: (a) the decrease in the laser fluence along the jet due to the absorption by O2 in the gas mixture, (b) the increase in temperature, and consequent decrease in gas density, as a result of energy released in the photochemical and chemical processes that occurred, and (c) the formation of OH(v = 0) as a result of relaxation, particularly by O2, of OH radicals formed in levels v > 0. Once these corrections were made, the rate constant for reaction between OH and O(3P) atoms showed little variation in the temperature range of 142 to 39 K and had a value of (3.5 +/- 1.0) x 10(-11) cm3 molecule(-1) s(-1). It is recommended that this value is used in future chemical models of dense interstellar clouds.     

Fixed points of uniformly lipschitzian mappings

Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lifšic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lifšic’s theorem gives a sharper result. Also, a new property is introduced that yields a fixed point theorem for uniformly lipschitzian mappings in a class of hyperconvex spaces, a class which includes those possessing property (P)$\left(P\right)$ of Lim and Xu.     

Lieb–Robinson Bounds for the Toda Lattice

We establish locality estimates, known as Lieb–Robinson bounds, for the Toda lattice. In contrast to harmonic models, the Lieb–Robinson velocity for these systems do depend on the initial condition. Our results also apply to the entire Toda as well as the Kac-van Moerbeke hierarchy. Under suitable assumptions, our methods also yield a finite velocity for certain perturbations of these systems.     

Dynamical Localization in Disordered Quantum Spin Systems

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective one-particle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized.